A first-principles study of weakly bound molecules using exact exchange and the random phase approximation.

We present a study of the binding energy (BE) curves of rare gas and alkaline-earth dimers using an energy functional that includes exact exchange (EXX) and correlation energies within the random phase approximation (RPA). Our results for the equilibrium positions and long range behavior of the potential energy curves show great improvements over those obtained at the density functional theory level, within local and semilocal approximations. BEs are improved as well in the case of rare gas dimers. For Ar and Kr, the accuracy of our results is comparable to that of so-called van der Waals density functionals, although EXX/RPA yields BE curves that agree better with experiment for large separation distances, as expected. We also discuss shortcomings of the EXX/RPA perturbative approach and analyze possible sources of error in the description of the potential energy curve of alkaline-earth dimers, in particular, Be(2), exhibiting an unphysical maximum at large separations. We suggest that the lack of self-consistency in current EXX/RPA approaches might be largely responsible for most of the observed shortcomings. Finally, we present a tight-binding approach to obtain the eigenvalues of the dielectric matrix entering the calculation of the RPA correlation energy that greatly improves the efficiency of EXX/RPA calculations.